Abstract
The structured singular value (SSV or μ) is known to be an effective tool for assessing robust performance of linear time-invariant models subject to structured uncertainty. Yet all a single μ analysis provides is a bound β on the uncertainty under which stability as well as H ∞ performance level of k/β are guaranteed, where k is preselect able. In this paper, we introduce a related quantity, denoted by v which, for a given β, provides a value α such that for any uncertainty bounded by β an H ∞ performance level of α (but none better than α) is guaranteed.
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This work was supported in part by the National Science Foundation’s Engineering Research Centers Program: NSFD CDR-88-03012, by the NSF under Grant DMC-85-51515, and by Rockwell International.
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References
J.C. Doyle, J.E. Wall & G. Stein, “Performance and Robustness Analysis for Structured Uncertainty,” in Proc. 21st IEEE Conf. on Decision and Control, Orlando, Florida, December 1982, 629–636.
J.C. Doyle, “Analysis of Feedback Systems with Structured Uncertainties,”Proc. IEE-D129 (1982), 242–250.
M.K.H. Fan & A.L. Tits, “Characterization and Efficient Computation of the Structured Singular Value,” IEEE Trans. Automat. Control AC-31 (1986), 734–743.
M.K.H. Fan, A.L. Tits & J.C. Doyle, “Robustness in the Presence of Joint Parametric Uncertainty and Unmodeled Dynamics,” in Proc. of the 1988 American Control Conference, Atlanta, Georgia, June 1988, 1195–1200.
M.K.H. Fan, A.L. Tits & J.C. Doyle, “Robustness in the Presence of Mixed Parametric Uncertainty and Unmodeled Dynamics,” IEEE Trans. Automat. Control 36 (January 1991, to appear).
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© 1991 Springer Science+Business Media New York
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Fan, M.K.H., Tits, A.L. (1991). Worst-Case H ∞ Performance Under Structured Perturbations with Known Bounds. In: New Trends in Systems Theory. Progress in Systems and Control Theory, vol 7. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-0439-8_33
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DOI: https://doi.org/10.1007/978-1-4612-0439-8_33
Publisher Name: Birkhäuser, Boston, MA
Print ISBN: 978-1-4612-6760-7
Online ISBN: 978-1-4612-0439-8
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